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Chapter 2: Q65E (page 155)

Draw the graph of the function f (x) = [x] + [x/2] from R to R.

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Most popular questions from this chapter

Determine whether each of these functions is a bijection from R to R.

  1. fx=2x+1
  2. fx=x2+1
  3. fx=x
  4. fx=x2+1/x2+2

Define the product of two matrices A and B. When is this product defined?

Suppose that g is a function from A to B and f is a function from B to C.

  1. Show that if both f and g are one-to-one functions, thenf∘gis also one-to-one.
  2. Show that if both f and g are onto functions, then f∘g is also onto.

Question: Consider these functions from the set of students in a discrete mathematics class. Under what conditions is the function one-to-one if it assigns to a student his or her

  1. Mobile phone number

  2. Student identification number

  3. Final grade in the class

  4. Home town.

Prove or disprove each of these statements about the floor and ceiling functions.

  1. [⌊x⌋⌉=⌊x⌋for all real numbers x.
  2. ⌊2x⌋=2⌊x⌋whenever x is a real number.
  3. ⌈x⌉+⌈y⌉−⌈x+y⌉=0or1whenever x and y are real numbers.
  4. ⌈xy⌉=⌈x⌉⌈y⌉for all real numbers x and y.
  5. x2=x+12for all real numbers x.
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